Optimization Of Dynamic Vibration Absorber Research Articles

Adaptive multiswarm particle swarm optimization for tuning the parameter optimization of a three-element dynamic vibration absorber

Abstract. A reliable optimization of dynamic vibration absorber (DVA) parameters is extremely important to analyze its dynamic damping characteristics and improve its vibration suppression performance. In this paper, we will discuss a parameter optimization method of the Voigt and three-element DVA models according to the H∞ optimization criterion. The particle swarm optimization method is an effective heuristic optimization algorithm; however, it is easy to lose diversity and fall into local extremum. To solve this problem, the adaptive multiswarm particle swarm optimization (AM-PSO) is used to search the solution of the DVA models. Particles in AM-PSO are adaptively divided into multiple swarms, and the variable substitution learning strategy is utilized to reduce their computational complexity and improve the algorithm's global search capability. In addition, the AM-PSO method is employed to optimize the parameters of DVA models and compared with the genetic algorithm and PSO. The simulation results show that the AM-PSO algorithm has superior performance. Also, the adaptive multiswarm numerical design method discussed herein will push the field towards practical applications, including traditional DVA and related complex three-element DVA.

Parameters optimization of dynamic vibration absorber based on grounded stiffness, inerter, and amplifying mechanism

In the field of dynamics and control, some typical vibration devices, including grounded stiffness, inerter and amplifying mechanism, have good vibration isolation and reduction effects, especially in dynamic vibration absorber (DVA). However, most of the current research studies only focus on the performance of a single device on the system, and those DVAs are gradually becoming difficult to meet the growth of performance demand for vibration control. On the basis of Voigt dynamic vibration absorber, a novel dynamic vibration absorber model based on the combined structure of grounded stiffness, inerter, and amplifying mechanism is presented, and the analytical solution of the optimal design formula is derived. First, the motion differential equation of the system is established, and the normalized amplitude amplification factor of the displacement is calculated. It is found that the system has three fixed points unrelated to the damping ratio. The optimal frequency ratio is obtained based on the fixed-point theory. In order to ensure the stability of the system, it is found that inappropriate inerter coefficient will cause the system instable when screening optimal grounded stiffness ratio. Accordingly, the best working range of inerter is determined. Finally, optimal grounded stiffness ratio and approximate optimal damping ratio are also obtained. The influence of inerter coefficient and magnification ratio on the response of the primary system is analyzed. The correctness of the derived analytical solution is verified by numerical simulation. Compared with other dynamic vibration absorbers, it is verified that presented model has superior vibration absorption performance and provides a theoretical basis for the design of a new type of dynamic vibration absorbers.

Closed-form solutions to the optimization of dynamic vibration absorber attached to multi-degrees-of-freedom damped linear systems under torsional excitation using the fixed-point theory

Traditional design optimization of the Voigt-type dynamic vibration absorber often solved for the vertical or lateral vibration problems. However, for the damped primary system under torsional excitation, to the best of our knowledge, there is no study to solve this problem by algebraic approaches. This paper presents the analytical solutions to the optimization of dynamic vibration absorber, which is used to suppress torsional vibration of multi-degrees-of-freedom damped linear systems. The parameters considered in optimizing are dimensionless natural frequency of dynamic vibration absorber and viscous damping of absorber. First, the system equations of motion for shaft–dynamic vibration absorber system subjected to time-varying torsional moment were established. Then, closed-form formulae of optimized parameters were derived using the fixed-point theory. The obtained formulae provide exact solution for the proposed problem. To confirm the effectiveness of the obtained formulae, parametric studies on torsional vibration were performed for several sample multi-degrees-of-freedom systems with and without optimal dynamic vibration absorber. Numerical results showed that torsional vibrations of the primary system attached with optimal dynamic vibration absorber are effectively suppressed, even in the resonant conditions.

Design Optimization of Dynamic Vibration Absorber for Damped System Subjected to Random Excitation

Design Optimization of Dynamic Vibration Absorber for Damped System Subjected to Random Excitation

Closed-Form Exact Solution to H∞ Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems)

H ∞ optimization of the dynamic vibration absorbers is a classical optimization problem, and has been already solved more than 50 years ago. It is a well-known solution, but we know this solution is only an approximate one. Recently, one of the authors has proposed a new method for attaining the H∞ optimization of the absorber in linear systems. The new method enables us to obtain the exact algebraic solution of the H∞ optimization problem of the absorber. In this paper, we first apply this method to the design optimization of a viscous damped (Voigt type) absorber and a hysteretic damped absorber attached to undamped primary systems. For each absorber, six different transfer functions are taken here as performance indices to vibration suppression or isolation. As a result, we found the closed-form exact solutions to all transfer functions. The solutions obtained here are then compared with those of the approximate ones. Finally, we present the closed-form exact solutions to the hysteretic damped absorber attached to damped primary systems.

Analytical Solutions to H∞ and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems

AbstractH ∞ and H2 optimization problems of the Voigt type dynamic vibration absorber (DVA) are classical optimization problems, which have been already solved for a special case when the primary system has no damping. However, for the general case including a damped primary system, no one has solved these problems by algebraic approaches. Only the numerical solutions have been proposed until now. This paper presents the analytical solutions for the H∞ and H2 optimization of the DVA attached to the damped primary systems. In the H∞ optimization the DVA is designed such that the maximum amplitude magnification factor of the primary system is minimized; whereas in the H2 optimization the DVA is designed such that the squared area under the response curve of the primary system is minimized. We found a series solution for the H∞ optimization and a closed-form algebraic solution for the H2 optimization. The series solution is then compared with the numerical solution in order to check the accuracy in connection with the truncation error of the series. The exact solution presented in this paper is too complicated to handle by a hand-held calculator, so we proposed an approximate solution for the practical object.

Exact Algebraic Optimization of a Dynamic Vibration Absorber for Minimization of Maximum Amplitude Response. 1st Report. Viscous Damped Absorber.

Recently, Nishihara and Matsuhisa have proposed a new theory for attaining the H∞ optimization of a dynamic vibration absorber(DVA)in the linear vibratory systems. This is a classical optimization problem, and already solved more than 50 years ago using the so-called fixed-points theory. However, this solution is only an approximate one for the H∞ optimization of DVA. The new theory proposed them gives us the exact solution. Using this theory, they found the closed-form exact solution for a typical performance index, namely, compliance transfer function of the system. In this paper, we will apply this theory to another performance indexes : mobility and accelerance transfer functions for force excitation system, and the absolute and relative displacement responces to acceleration, velocity or displacement input to foundation for motion excitation system. As a result, we found the closed-form exact solutions for all performance indexes described above when the primary system has no damping. The results obtained here are compared with the approximate ones derived by the fixed-points theory.

Accelerance Minimization of Passive Vibration Control Mechanisms by Fixed Points Theory. Design Optimization of Dynamic Vibration Absorber and Passive Gyroscopic Damper.

The design optimization of passive vibration control mechanisms in the accelerance domain is discussed. In this study, the fixed points theory is developed which approximately minimizes the maximum accelerance in the frequency domain by equally adjusting the accelerance of two fixed points. This design method is applied to the dynamic vibration absorber (DVA) and the passive gyroscopic damper (PGD), and thus the maximum accelerances of these mechanisms are successfully reduced. The concept of the fixed points theory is reinvestigated. The accuracy and the degree of improvement compared with the fixed points design in the compliance domain are examined. The PGD realizes relatively higher damping effects, and then the accelerance reduction of the PGD by the new design method is considerably larger than that of the DVA with a moderate mass ratio.